Communications of the
Korean Mathematical Society CKMS

A graph $G$ is called a well covered graph if every maximal independent set in $G$ is maximum, and co-well covered graph if its complement is a well covered graph. We study some properties of a co-well covered graph and we characterize when the join, the corona product, and cartesian product are co-well covered graphs. Also we characterize when powers of trees and cycles are co-well covered graphs. The line graph of a graph which is co-well covered is also studied.

Keywords: Well covered graphs, co-well covered graphs, cliques

MSC numbers: 05C69 and 05C75